A045532 Concatenate n with n-th prime.

12, 23, 35, 47, 511, 613, 717, 819, 923, 1029, 1131, 1237, 1341, 1443, 1547, 1653, 1759, 1861, 1967, 2071, 2173, 2279, 2383, 2489, 2597, 26101, 27103, 28107, 29109, 30113, 31127, 32131, 33137, 34139, 35149, 36151, 37157, 38163, 39167, 40173, 41179, 42181

Offset: 1

Author

Jeff Burch

Keywords

• nonn
• base

Comments

Triangular numbers are 1653, 32131, 79401, ... - Ali Adams, Feb 04 2020

The next such terms are 173340627863131 and 1454987833022905581. - Giovanni Resta, Feb 04 2020

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A075110.

Cf. A085451. [Reinhard Zumkeller, Jun 30 2010]

Programs

Haskell

a045532 n = read $ show n ++ show (a000040 n) :: Integer
-- Reinhard Zumkeller, Jul 08 2014

Magma

[Seqint(Intseq(NthPrime(n)) cat Intseq(n)): n in [1..45]]; // Vincenzo Librandi, Apr 13 2019

Mathematica

Table[FromDigits[Join[IntegerDigits[n], IntegerDigits[Prime[n]]]], {n, 40}] (* Vincenzo Librandi, Apr 13 2019 *)
#[[1]]*10^IntegerLength[#[[2]]]+#[[2]]&/@Table[{n,Prime[n]},{n,50}] (* Harvey P. Dale, Oct 11 2024 *)

PARI

a(n) = eval(Str(n,prime(n))); \\ Michel Marcus, Apr 13 2019, simplified by M. F. Hasler, Feb 05 2020

Python

from sympy import prime
def a(n): return int(str(n) + str(prime(n)))
print([a(n) for n in range(1, 43)]) # Michael S. Branicky, Dec 23 2021

Formula

a(n) = n*10^(A004216(A000040(n))+1) + A000040(n). - Reinhard Zumkeller, Sep 03 2002